# A relativistic quantum theory of gravity

by meopemuk
Tags: gravity, quantum, relativistic, theory
P: 1,746
 Quote by yogi Decided to accept your invitation. First, my own views are similar - I don't think its unjustified to propose field action at a distance - logically it seems to make more sense than conjuring up spin 2 virtual particles - virtual photons all got started with Feynman as an alternative to calculating the perturbation coefficients - then it got carried over to gravity - but I cannot believe that these concepts are more that metaphorical at best.
Hi Yogi,

You are right, virtual photons of QED are methaphorical non-observable concepts. The entire theory can be recast in the action-at-a-distance form without losing the accuracy of its predictions. This is done in a systematic way in

E.V. Stefanovich "Relativistic quantum dynamics", http://www.arxiv.org/physics/0504062

which is based on the "dressed" (or "clothed") particle approach first proposed in

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim. 8 (1958), 378

and developed further by L. D. Faddeev, M. I. Shirokov, and few others.

Eugene.
P: 1,941
 Quote by sweetser Relativistic quantum field theory is all about the particles that mediate the interaction. One uses the propagator to calculate scattering angles in Feynman diagram calculations. It makes no sense to say you have a quantum field theory without a mediating particle.
For the record, relativistic QFT is not "all" about the particles that mediate
the interaction. E.g: phi^4 QFT has no mediating particle but we can still
calculate scattering amplitudes. However, the phi^4 interaction remains
local, whereas Eugene's proposed interaction is non-local.

 It's like saying one has an approach to QED without the photon.
Actually, it's not really like that. In QED we can observe photons, whereas
gravitons and gravity-waves are still a bit controversial. If they are
unambiguously discovered, Eugene's theory will be in trouble and/or require
modification.
P: 1,746
 Quote by strangerep In QED we can observe photons, whereas gravitons and gravity-waves are still a bit controversial. If they are unambiguously discovered, Eugene's theory will be in trouble and/or require modification.
There is an indirect proof of existence of free (not virtual!) gravitons and gravitational waves in observations of the orbital decay in binary pulsar systems, e.g.,

M. Kramer, et al. "Tests of general relativity from timing the double pulsar" http://www.arxiv.org/astro-ph/0609417

You are right, if graviton radiation is indeed discovered, this would mean a mild (but manageable) trouble for my theory. There would be no need to change the present (instantaneous) potential form of mass-mass and mass-photon interactions. The theory could be fixed by adding extra terms to the Hamiltonian. These terms would describe the graviton emission and absorption. In the lowest order they might have the form

a*a*aag + a*a*g*aa

where a*/a are creation/annihilation operators of massive particles and g*/g are creation/annihilation operators of gravitons. This form of the Hamiltonian would be quite similar to the QED Hamiltonian in the "dressed particle" approach discussed in my previous post.

Eugene.
 P: 1,480 The binary pulsar decay may be a case of experimenters finding what they want to find. The problem I have with all force field communications is that there is no model of how forces can be connected this way - if a photon is emitted it travels by a well defined relationship with the properties of free space - it leaves here and it goes there - and it impacts and transfers momentum - in a field, something starts at A, travels to B - but it is still at A Force fields cannot be imagined as particles going from A to B, yet most modern physics mathamatically models these fields the same way as light - I think Eugene's approach is a step in a direction that could lead to a holistic viewpoint of force fields in general I am curious whether Van Flanderen published a response to Carlip's paper?
P: 1,746
 Quote by yogi The binary pulsar decay may be a case of experimenters finding what they want to find.
There was a Nobel prize awarded for measurements and GR explanations of binary pulsar properties (including the orbital decay). That's not easy to beat.

 Quote by yogi Force fields cannot be imagined as particles going from A to B, yet most modern physics mathamatically models these fields the same way as light
I think most serious QFT practitioners do not accept virtual particles as real concepts. They are just internal lines in Feynman diagrams, or certain factors (propagators) in Feynman integrals. No more than that. The trouble arises when someone tries to "explain" Feynman diagrams to laymen. Then all this nonsense about "interaction carriers" and "virtual particle exchanges" begins.

 Quote by yogi I am curious whether Van Flandern published a response to Carlip's paper?
There is a (relatively) recent paper

T. Van Flandern, J. P. Vigier, "Experimental repeal of the speed limit for gravitational, electromagnetic, and quantum field interactions", Found. Phys. 32 (2002), 1031.

where he discusses Carlip's response. In my opinion, the debate Van Flandern - Carlip is in a dead end.

Van Flandern basically says (rephrased): "there is no aberration in gravitational interaction, i.e., the force of gravity points to the instantaneous position of the source, not to the retarded position. Therefore, the propagation of gravity must be instantaneous"

Carlip replies (rephrased): "Yes, there is no aberration of gravity (this is an experimental fact), but this doesn't prove the instantaneous propagation of gravity. In GR, if you take into account velocity dependent terms of higher orders in $c^{-2}$, then, due to some lucky compensation, the total force does not have aberration, even though all terms are retarded."

I think that Carlip is right. Aberration does not necessarily implies the superluminal propagation of the force. So, one cannot decide one way or the other by looking only at aberration.

You are probably aware of Fomalont and Kopeikin recent measurements of the light deflection by Jupiter. They claimed that they have measured the speed of gravity that coincided with c. There is a lot of responses to this result (some references are in my paper), which argue that the speed of light was actually measured, rather than the speed of gravity. I am lacking deep knowledge of GR, so I can't appreciate the arguments in this debate. I was thinking about calculating this effect within my theory. This should be a good independent check of its validity. What do you think?

Eugene.
 P: 1,480 Yes - I am aware of the Kopeikin claim - and also the criticisms thereof. If you can come up with numbers, critics take notice. I do not have your article in front of me at present - have you included a critique of Einstein's explanation of the perihelion precession of Mercury's orbit. I have read some criticism of how he used this to validate the c velocity of gravitational propagation - I need to reread your paper on this. In any event - you are in for an uphill battle. Had not realized the binary pulser data got a Nobel - I would say premature. Feynman got one too - as he said: "For sweeping the infinities under the rug" One of the problems in handing out such awards is that it blesses the work with an air of infallibility There are several issues that arise in connection with G fields - one is how fast the new position of an object is communicated to other masses when it moves, or when it accelerates or when the accelertion changes. Another is, if a particle is destroyed - how fast is this information communicated. These may each involve different kinds of propagation mechanisms. Then there is the interesting question of what is the nature of the de Broglie wave when matter is accelerated. Think how boring physics would be if all the problems were solved. How lucky we are to be able to ponder these questions.
P: 1,746
Hi, Yogi,

 Quote by yogi I do not have your article in front of me at present - have you included a critique of Einstein's explanation of the perihelion precession of Mercury's orbit. I have read some criticism of how he used this to validate the c velocity of gravitational propagation - I need to reread your paper on this. In any event - you are in for an uphill battle.
No, I don't discuss or criticize Einstein's general relativity in the paper. I also believe that predictions made in GR are perfectly consistent within this approach. This theory made a huge number of correct predictions without any fitting parameters. This is truly amazing! And this makes so much harder to come up with an alternative theory.

Nevertheless, I believe that GR is built on wrong physical premises (the 4D space-time manifold) and sooner or later this will show up in disagreements with experiments. For example, I discuss possible violations of the equivalence principle in section 5.1.

 Quote by yogi Had not realized the binary pulser data got a Nobel - I would say premature. Feynman got one too - as he said: "For sweeping the infinities under the rug" One of the problems in handing out such awards is that it blesses the work with an air of infallibility

In 1993 Taylor and Hulse received the Nobel prize for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation. This was a remarkable piece of work, and I wouldn't say that the prize was premature. Likewise, the development of the renormalized QED in the late 1940's was probably the greatest advance in theoretical physics after formulation of quantum mechanics in 1926. Of course, this doesn't mean that the final judgement has been pronounced on these matters.

 Quote by yogi There are several issues that arise in connection with G fields - one is how fast the new position of an object is communicated to other masses when it moves, or when it accelerates or when the accelertion changes. Another is, if a particle is destroyed - how fast is this information communicated. These may each involve different kinds of propagation mechanisms.
I believe that gravitational interactions propagate instantaneously, however, I don't know any convincing way to demonstrate that experimentally. I think, there is much greater chance to confirm the superluminal propagation of electromagnetic interactions. In recent years there has been a large number of experiments pointing in this direction.

 Quote by yogi Think how boring physics would be if all the problems were solved. How lucky we are to be able to ponder these questions.
I thank "Supreme Being" everyday for the privilege to live in such interesting times.

Eugene.
 P: 361 Hello Eugene: The Lorentz transformations are part of the machinery that characterizes the Lorentz group. That group is not approximate. It is the group that every observation ever made in regards to special relativity is based. If you decide to ditch the Lorentz group, well, you are not going to have friends. Superluminal propagation of interactions does create problems for causality. There are plenty of reasons not to like tachyon theory. doug
P: 1,746
Hello doug,

 Quote by sweetser The Lorentz transformations are part of the machinery that characterizes the Lorentz group.
I respectfully disagree. The Lorentz group and Lorentz transformations are two separate issues, and they are not 100% equivalent

Lorentz group is a 6-parameter group of transformations between inertial observers (it includes rotations and boosts). It is a subgroup of the full 10-parameter Poincare group of inertial transformations, which, in addition, includes space and time translations. The Poincare group is an exact set of relationships. Any physical system, interacting or otherwise, must be invariant with respect to Poincare group transformations. We agree 100% about that. In quantum mechanics, this means that the Hilbert space of any physical system should carry an unitary representation of the (universal covering of the) Poincare group.

Lorentz transformations are certain formulas that connect space-time coordinates of events in different moving reference frames. For example, if observer O sees and event at point x at time t, then, according to Lorentz transformations, observer O' moving relative to O with velocity v sees the same event at the space-time point (x', t'), where

$$x' = (x -vt)(1-v^2/c^2)^{-1/2}$$..........(1)
$$t' = (t - xv/c^2)(1-v^2/c^2)^{-1/2}$$......(2)

I prefer a slightly different notation in which velocity v is replaced by rapidity $\theta$, such that $v = c \tanh \theta$. Then

$$x' = x \cosh \theta - ct \sinh \theta$$.........(1')
$$t' = t \cosh \theta - x/c \sinh \theta$$........(2')

My point is that transformations (1)-(2) or (1')-(2') do not follow immediately from properties of the Lorentz (or Poincare group). Some additional assumptions should be made to make such a derivation, and these are crucial assumptions. For example, one situation in which Lorentz transformations (1)-(2) can be rigorously proven is when particles (whose worldline points and collisions form the events in question) are non-interacting. However, transformations of space-time coordinates of such events become different from simple formulas (1)-(2) if interaction between particles is turned on. I briefly discuss this point in section 5.2 of the paper. A more detailed discussion can be found in section 10.2 of http://www.arxiv.org/physics/0504062.

The difference between the concepts of relativistic invariance (the Lorentz and Poincare groups) and manifest covariance (Lorentz transformations) has been known for a long time. I strongly recommend this paper

D. G. Currie, T. F. Jordan, E. C. G. Sudarshan, "Relativistic invariance and
Hamiltonian theories of interacting particles", Rev. Mod. Phys., 35 (1963), 350

where these two concepts are discussed with outmost clarity. In particular, the authors prove an interesting theorem which says that in a relativistic theory of classical particles their worldlines can transform by Lorentz formulas (1)-(2) only if interaction is absent.

 Quote by sweetser That group is not approximate. It is the group that every observation ever made in regards to special relativity is based. If you decide to ditch the Lorentz group, well, you are not going to have friends.
As I said I fully accept the exact and universal character of the Lorentz group. However, I do not accept the exact and universal character of Lorentz transformations for space-time coordinates of events. I don't think there is a contradiction in my position.

 Quote by sweetser Superluminal propagation of interactions does create problems for causality.

The problems with causality arise if one applies Lorentz transformations (1)-(2) (which are strictly valid for non-interacting systems only) to an interacting system. If one properly takes into account the interaction-dependence of boost transformations, then these problems disappear. I briefly discuss this point in section 5.3 of the paper. A more detailed discussion can be found in section 10.2 of http://www.arxiv.org/physics/0504062.

 Quote by sweetser There are plenty of reasons not to like tachyon theory.
I don't like tachyon theory as well. However, note that we have discussed the superluminal propagation of interactions, not particles. Interactions can propagate superluminally, particles can't.

Eugene.
 P: 1,480 "In 1993 Taylor and Hulse received the Nobel prize for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." As I understand the results, they were very close to the desired fit on only one pulsar pair - maybe there are more recent tests. If your action at a distance theory is correct, there is no justification for gravitational waves. But of course you are already aware of that. "....the development of the renormalized QED in the late 1940's was probably the greatest advance in theoretical physics after formulation of quantum mechanics in 1926. Of course, this doesn't mean that the final judgement has been pronounced on these matters." It gives very close correlation to the measured values - but It is ad hoc from the standpoiint of a physical explanation. With regard to the Lorentz tranforms cited by sweetser - I have yet to see an experiment that establishes the truth of those parts of the transforms that are the result of the one way velocity of light - what is proven is the invarience of the interval - but this is easily obtained from Minkowski unification which leads to the result that the two way velocity is constant. Selleri spend most of his later years reviewing the known experiments dealing with SR time dilations and concluded they could all be easily explained with simple inertial transforms without reference to the xv/c^2 term that arises from the one way constancy postulate. While Lorentz-Einstein transforms may be correct, there needs to be a distinguishing experiment one that invalidates either Selleri or Einstein. I raise this because it bears on the issue of synchronization and consequently causality ...when information travels faster than light, the causalty issue does not occur in Selleri transforms.
P: 1,746
 Quote by yogi "In 1993 Taylor and Hulse received the Nobel prize for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." As I understand the results, they were very close to the desired fit on only one pulsar pair - maybe there are more recent tests.
Yes, more binary systems were discovered since then, including those in which both neutron stars are seen as pulsars from Earth. A lot of new data has been accumulated, all of which is consistent with GR. Check this recent reference:

M. Kramer et al. "Tests of general relativity from timing the double pulsar",
http://www.arxiv.org/astro-ph/0609417

 Quote by yogi If your action at a distance theory is correct, there is no justification for gravitational waves. But of course you are already aware of that.
Yes, gravitational waves are not needed in my approach. However, there is still a puzzle related to the observed orbital decay of binary pulsar systems. This seems to be a real effect, which indicates that energy gets radiated away in some form. There was no direct observation of this radiation, so we don't know what it is. The usual viewpoint is that this is the gravitational radiation. It could be also possible that this is a low-energy electromagnetic radiation. Both these possibilities can be, in principle, accomodated within my approach by adding extra terms to the Hamiltonian. (I discussed this point in post #21.) I would prefer the latter possibility, because I don't like the idea of introducing new particles (gravitons).

 Quote by yogi "....the development of the renormalized QED in the late 1940's was probably the greatest advance in theoretical physics after formulation of quantum mechanics in 1926. Of course, this doesn't mean that the final judgement has been pronounced on these matters." It gives very close correlation to the measured values - but It is ad hoc from the standpoiint of a physical explanation.
I have a much higher opinion about renomalized QED of Tomonaga-Schwinger-Feynman. I expressed my views in detail in chapters 9 and 12 of http://www.arxiv.org/physics/0504062.

Briefly, I think the trouble began already in the original formulation of QED (late 1920's). The Hamiltonian of this theory was derived from vague analogies with Maxwell's electrodynamics, and this Hamiltonian didn't satisfy some very important physical principles (the stability of vacuum and 1-particle states). This Hamiltonian was useless for S-matrix calculations beyond the leading perturbation order, because of infinities.

Tomonaga, Schwinger, and Feynman fixed a part of this problem in the late 1940's. They added infinite counterterms to the original Hamiltonian in such a way that all infinities in the S-matrix canceled out and very precise agreement with experiment could be achieved. However, as you said, they "swept infinities under the rug". This rug was the Hamiltonian. In renormalized QED, the Hamiltonian has infinite terms, so it is useless for anything but S-matrix calculations.

Another improvement of QED is needed in order to obtain both reasonable Hamiltonian and accurate S-matrix. This can be done by using the "dressed particle" approach. This approach has been known for a long time

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim., 8 (1958), 378.

Unfortunately, it didn't get much traction in modern quantum field theories.

 Quote by yogi Selleri spend most of his later years reviewing the known experiments dealing with SR time dilations and concluded they could all be easily explained with simple inertial transforms without reference to the xv/c^2 term that arises from the one way constancy postulate. While Lorentz-Einstein transforms may be correct, there needs to be a distinguishing experiment one that invalidates either Selleri or Einstein. I raise this because it bears on the issue of synchronization and consequently causality ...when information travels faster than light, the causalty issue does not occur in Selleri transforms.
Unfortunately, it is very difficult to verify Lorentz transformations themselves. Experiments can only probe some of their consequences, such as the time dilation. I haven't heard about Selleri's works. Do you have a reference?

ADDED: Perhaps the most important idea that I had in my works is that there can be no unique and universal formula for boost transformations of particle observables (such as the formula for Lorentz transformations). Boost transformations should depend on the system in which these transformations are measured and on interactions acting in the system. That's why I am sceptical about attempts to find a universal transfrormation.

Thanks.
Eugene.
P: 1,746
 Quote by yogi I recalled that you had derived the perihelion motion - so I pulled up your article and re-read that part - you have treated this and found your derivation consistent with the observations - that is a big plus.

Yes, I used a fairly simple instantaneous potential Sun-Mercury, which consisted of the usual Newtonian part plus small velocity-dependent correction. The important part was to make sure that this potential satisfies the principle of relativistic invariance (commutation relations of the Poincare Lie algebra). Otherwise, it was simply fitted to reproduce the observed shift of the Mercury's perihelion. I want to emphasise that I didn't formulate this interaction from some first principles, and then found that the calculated perihelion precession agrees with measurements. Not at all. That would be a really great accomplishment, and I don't claim that.

What I have done in this paper is, simply, a proof of principle. I wanted to show that one can, in principle, find an instantaneous gravitational potential, which satisfies all requirements that I formulated in the beginning of the paper (relativistic invariance, unitarity, agreement with experiment, etc.). In fact, I believe, that one can write many different potentials that would satisfy all these requirements. Currently, I have no idea what additional fundamental principles are needed, which would select just one true potential.

My primary objective was to break the monopoly of GR on explanation of experimental facts. I wanted to show that there is a much wider class of acceptable theories, which agree with existing observations. It is even more important that some of these theories are perfectly compatible with quantum mechanics, which is not true for GR.

 Quote by yogi I guess my only suggestion would be to de-emphasize the action at distance premise since you have alternatives.
This is something that I wouldn't like to do, because all interactions in my approach are true action-at-a-distance interactions. As I said earler, I don't exclude the possibility of radiation of free gravitons. But this possibility doesn't change a bit the instantaneous (non-retarded) character of interactions between massive bodies. In other words, gravitons can exist as free particles in my approach, but there is no place for them as "virtual interaction carriers".

 Quote by yogi But you raise a good point in that, while there is slowing of binary systems, - it doesn't mean necessarily that it takes the form of gravitational radiation - for all we know it the energy may be absorbed in some form of dark matter
I remain agnostic regarding the physical nature of radiation emitted by binary pulsars. My first choice would be the usual electromagnetic radiation. If this is true, then there should be an unexplained bump somewhere in the EM emission spectrum of the binary system, and the integrated radiation power under this bump should match the energy loss calculated from the orbital decay. That's all I can speculate about regarding this possibility. The second choice would be the emission of gravitons, but this choice is less attractive due to the speculative nature of these particles.

 Quote by yogi My own view is consistent with GR in part - in that masses condition space - they do not act directly upon one another. As you probably know, there are several authors including Sciama, that have developed theories to explain inertia in terms of Mach's principle - all such theories require instant action at a distance - so you might want to read some of these if you have not already done so. I will send you a link to one of Selleri's articles. Selleri is not accepted by main stream, nor as you know, is Van Flanderen. Selleri however, has a list of accomplishments a mile long, so he can't be ignored summarily
I would appreciate your sending me references to Sciama and Selleri.

Thank you.
Eugene.
 P: 1,480 Eugene - try this link oldserver.ba.infn.it/~selleri/ - 10k Articles R39 and R27 should be of some interest. If That Link doesn't work, you can google Franco Selleri and get a lot of his papers Would be interested in your opinion on the inertial transforms - Yogi
 P: 1,480 Just checking - looks like that link is incomplete - i will try to get it right
P: 1,746
 Quote by yogi Eugene - try this link http://oldserver.ba.infn.it/~selleri/ - 10k Articles R39 and R27 should be of some interest. If That Link doesn't work, you can google Franco Selleri and get a lot of his papers Would be interested in your opinion on the inertial transforms - Yogi
Hi Yogi,

thank you for the link to Selleri's papers. I read the paper R39

F. Selleri, "Recovering the Lorentz Ether", Apeiron 11 (2004), 246

where he proposes "inertial transformations" that are supposed to replace "Lorentz transformations" of special relativity. I have quite a few objections to different statements in this paper. I'll mention just two objections, which look the most obvious to me:

1. His "inertial transformations" imply that the velocity of light should depend on the velocity of the light source. I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow.

2. Selleri is right that it is difficult to measure Lorentz transformations for the time and position of events in direct experiments. However, it is much easier to measure their cousins - Lorentz transformations for the momentum-energy of relativistic particles. These transformations have been observed in numerous particle experiments, and they form a foundation for relativistic particle kinematics established with great precision. I haven't noticed any discussion of "inertial transformations" for momentum-energy in the Selleri's paper. However, I suspect, that his version of such transformations would be also different from the special-relativistic experimentally established version.

Regards.
Eugene.

ADDED: Reading his other paper R27: "Bell's spaceships and special relativity" didn't change my opinion.
P: 1,746
 Quote by meopemuk I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow.
Here is the reference:

T. Alvager, F. J. M. Farley, J. Kjellman, I. Wallin, "Test of the second postulate of special relativity in the GeV region", Phys. Lett. 12 (1964), 260.

They directly measured (using the "time of flight" method) the velocity of gamma quanta emitted in decays of relativistic $\pi_0$ particles.

I can also recommend a good website with lots of references to experimental tests of special relativity

http://math.ucr.edu/home/baez/physic...periments.html

Eugene.
P: 1,480
 Quote by meopemuk Hi Yogi, thank you for the link to Selleri's papers. I read the paper R39 F. Selleri, "Recovering the Lorentz Ether", Apeiron 11 (2004), 246 where he proposes "inertial transformations" that are supposed to replace "Lorentz transformations" of special relativity. I have quite a few objections to different statements in this paper. I'll mention just two objections, which look the most obvious to me: 1. His "inertial transformations" imply that the velocity of light should depend on the velocity of the light source. I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow. Regards. Eugene. ADDED: Reading his other paper R27: "Bell's spaceships and special relativity" didn't change my opinion.
I dont know how you arrived at the conclusion that inertial transforms depend upon the source velocity. Selleri takes the position that the velocity of light is c in free space - his transforms avoid the postulate of one way light velocity - he embraces the proven part of the SR experiments - namely that MMx, Kennedy Thondyke etc are experiments confirming two way velocity

Can you direct me to the paragraph or words which you have relied upon to arrive at the above criticism?

Regards

Yogi

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